Question

When 0.728728728.… is converted into fraction, then what is its value?.

• A. $$\frac{7}{10}$$
• B. $$\frac{728}{999}$$
• C. $$\frac{72}{99}$$
• D. None of these

Answer 1

Answer:

$$\frac{728}{999}$$

Let x = 0.728728728…. → (1)

Here, 3 digits are repeating. Hence, 1000 should be multiplied on both sides.

1000x = 728.72872.... → (2)

Subtracting (1) from (2)

1000x - x =728.72872989... - 0.728728728....

999x = 728

$x=\frac{728}{999}$